Electric Potential IElectric Potential I

Physics 2113

Jonathan Dowling

Physics 2113 Physics 2113 Lecture 13: FRI 13 FEBLecture 13: FRI 13 FEB

Danger!

Volume [m3]

Area [m2]

Circumference [m]

Sphere

Circle

Cylinder

Electric Potential Electric Potential EnergyEnergyElectric Potential Energy U is Negative of the Work W to Bring Charges in From Infinity:

U = –W∞

The Change in Potential Energy ΔU Between an Initial and Final Configuration Is Negative the Work W Done by the Electrostatic Forces:

ΔU = Uf – Ui = –W

• What is the potential energy of a single charge? • What is the potential energy of a dipole? • A proton moves from point i to point f in a uniform electric field, as shown. - Does the electric field do positive or negative work on the proton? - Does the electric potential energy of the proton increase or decrease?

+Q –Qa

+Q

Electric Potential Electric Potential VoltageVoltageElectric potential voltage difference between two points

= work per unit charge needed to move a charge

between the two points:

ΔV = Vf – Vi = –W/q = ΔU/q

Electric Potential Energy vs Electric Potential Energy vs Electric Potential VoltageElectric Potential Voltage

Units :

Potential Energy = U = [J] = Joules

Potential Voltage = V = U/q = [J/C] = [Nm/C] = [V] = Volts

Electric Field = E = [N/C] = [V/m] = Volts per meter

Electron Volt = 1eV = Work Needed to Move an Electron

Through a Potential Difference of 1V:

W = qΔV = e x 1V = 1.60 10–19 C x 1J/C = 1.60 10–19 J

Electric Potential Voltage and Electric Potential Voltage and Electric Potential EnergyElectric Potential Energy

The change in potential energy of a charge q moving from point i to point f is equal to the work done by the applied force, which is equal to minus the work done by the electric field, which is related to the difference in electric potential voltage:

We move a proton from point i to point f in a uniform electric field, as shown.

• Does the electric field do positive or negative work on the proton? • Does the electric potential energy of the proton increase or decrease? • Does our force do positive or negative work ? • Does the proton move to a higher or lower potential?

Positive WorkPositive Work

Negative WorkNegative Work

+Q +Qa

+Q –Qa

Applied Positive Work:Applied Positive Work:Potential Energy Potential Energy

IncreasesIncreases

Applied Negative Work: Applied Negative Work: Potential Energy Potential Energy

DecreasesDecreases

+Q +Qa

+Q –Qa

Charge Moves Uphill:I’m doing work against Field.

Charge Moves Downhill:I’m Doing Work With Field

Work done by field is negative of Applied work done by me.

✔

✔

✔

✔

ICPP:ICPP:Consider a positive and a negative charge, freely moving in a

uniform electric field. True or false?

(a) Positive charge moves to points with lower potential.

(b) Negative charge moves to points with lower potential.

(c) Positive charge moves to a lower potential energy.

(d) Negative charge moves to a lower potential energy.

–Q +Q 0+V

–V

(a) True(b) False(c) True(d) True

+ + + + + + + + +

– – – – – – – –

✔

✔

✔

✔

electron

Electric Potential Energy, Electric Potential Energy, Electric PotentialElectric PotentialUnits :

Potential Energy = U = [J] = Joules

Electric Potential = V = U/q = [J/C] = [Nm/C] = [V] = Volts

Electric Field = E = [N/C] = [V/m] = Volts per meter

Electron Volt = 1eV = Work Needed to Move an Electron Through a Potential

Difference of 1V:

W = qΔV = e x 1V = 1.60 10–19 C x 1J/C = 1.60 10–19 J

Electric Potential Energy = JoulesElectric Potential Energy = JoulesElectric potential energy difference ΔU between two

points = work needed to move a charge between the

two points:

             ΔU = Uf – Ui = –W

Electric Potential Voltage = Volts = Electric Potential Voltage = Volts = Joules/Coulomb!Joules/Coulomb!

Electric potential — voltage! — difference ΔV between

two points = work per unit charge needed to move a

charge between the two points:

         ΔV = Vf – Vi = –W/q = ΔU/q

Equal-Potential = Equipotential SurfacesEqual-Potential = Equipotential Surfaces

• The Electric Field is Tangent to the Field Lines

• Equipotential Surfaces are Perpendicular to Field Lines

• Work Is Needed to Move a Charge Along a Field Line.

• No Work Is Needed to Move a Charge Along an Equipotential Surface (Or Back to the Surface Where it Started).

• Electric Field Lines Always Point Towards Equipotential Surfaces With Lower Potential.

Electric Field Lines and Equipotential SurfacesElectric Field Lines and Equipotential Surfaces

http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html

Why am I smiling?I’m About to Be

Struck byLightning!

Equipotential Surfaces: IPCCEquipotential Surfaces: IPCC

Conservative ForcesConservative ForcesThe potential difference between two points is independent of the path taken to calculate it: electric forces are “conservative”.

downhill

Summary:Summary:• Electric potential: work needed to bring +1C from infinity; units

V = Volt

• Electric potential uniquely defined for every point in space --

independent of path!

• Electric potential is a scalar — add contributions from individual

point charges

• We calculated the electric potential produced by a single

charge: V=kq/r, and by continuous charge distributions:

dV=kdq/r

• Electric potential energy: work used to build the system,

charge by charge. Use W=qV for each charge.